I've dabbled in this myself, making my own replacement parts for an antique wheel, and fixing up a second antique wheel.

If I were to build my own wheel from scratch with very low budget, I'd do a "walking wheel" which required far less pieces (doesn't need a foot petal or a flyer or a bobbin, the wheel is turned with one hand). It looks like the motherearthnews link (Koolbreeze's last link) is a walking wheel type made from a bicycle wheel. That seems reasonable to me as far as making it yourself as a novice. You can put a foot petal on if you want, but then it's called something else; I dont' know what the name is for a wheel that doesn't have a flyer (flyer is a U-shaped part with hooks on it that spins around a bobbin). I've never used that type of wheel, but they have a long history, and I could imagine working with one; some folks prefer them. One distinction is that the spun yarn is in front of the two posts, not between them, so you can see there is no bobbin required, it is just spun directly onto a shaft; it's much less part to manufacture!

Another GREAT low-cost way to go is to invest in a nice quality drop spindle. They're relatively cheap, and a real pleasure to spin with in their own right. You can spin on these while walking and chasing after kids, they are great fun, they're totally portable. You can literally spin while you go for a walk around the neighborhood. Knitty.com has an article on plying yarn that shows a handy method which would work well for plying from a drop spindle. (plying is the stage where you make your single ply into two-ply or three-ply yarn.) With this method you don't need another spindle to ply.

My second wheel was made by taking an antique wheel that had a good wheel and foundation, but none of the needed flyer parts. Instead of manufacturing parts as I did for my first wheel, I purchased an entire flyer unit for $99 from yarn.com (Ashford Traditional unit), and just mounted it to the wheel in place of original posts and flyer. If you can find a good base antique wheel with a 22" diameter wheel for $150 or less, this is an economical way to go, and you'll easily be able to get more bobbins and parts for the Ashford flyer, if you ever need it.

I know a new wheel costs a lot, but if I were to do it over, I wouldn't hesitate to invest in a wheel I love from the get-go. They don't devalue at all, in fact they can go up, it's amazing, so you can always just sell it if you tire of the hobby. I wouldn't get a wheel with the idea in mind that you'll save money on yarn enough to justify it, because you may not. But the wheel won't devalue if you take care of it, so you can consider it an investment and an asset. It's cheaper than a vacation, and it will bring you great pleasure to get one you really love. (And you still own the value of it, and can always sell it if you want to.)

Take a look at the Dodec Spinning Wheel (it's a spindle, not a bobbin, wheel) at http://porterthreads.weebly.com/ . No special wood-working tools needed: no lathe, no chisel. Very inexpensive (many would say "very inelegant," too, but hey!) and accessible. The designer has also produced videos showing the wheel in use.